With the ongoing development of new power systems, the integration of new energy sources is facing increasingly daunting challenges. The collaborative operation of shared energy storage systems with distribution networks and microgrids can effectively leverage the complementary nature of various energy sources and loads, enhancing energy absorption capacity. To address this, a shared energy storage capacity allocation method based on a Stackelberg game is proposed, considering the integration of wind and solar energy into distribution networks and microgrids. In this approach, a third-party shared energy storage investor acts as the leader, while distribution networks and microgrids serve as followers. The shared energy storage operator aims to maximize annual revenue, plan shared energy storage capacity, and set unit capacity leasing fees. Upon receiving pricing, distribution networks and microgrids aim to minimize annual operating costs, determine leased energy storage capacity, and develop operational plans based on typical daily scenarios. Distribution networks and microgrids report leasing capacity, and shared energy storage adjusts leasing prices, accordingly, forming a Stackelberg game. In the case study results, the annual cost of MGs decreased by 29.63%, the annual operating cost of the ADN decreased by 11.25%, the cost of abandoned light decreased by 60.77%, and the cost of abandoned wind decreased by 27.79% to achieve the collaborative optimization of operations. It is proven that this strategy can improve the economic benefits of all parties and has a positive impact on the integration of new energy.